Finite Group DatabasebetaFinite Group Databasebeta| order | 10340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D517 |
| unambiguous semidirect product | (D5×C11)⋊D47 |
| unambiguous semidirect product | (D5×C47)⋊D11 |
| Fitting, socle, derived, Hall | C5×C11×C47 ⋊ C22 |
| Hall | C11×C47 ⋊ C2×D5 |
| Hall | C5×C47 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D47 |
| Sylow | C47 ⋊ D5×D11 |
| Sylow | C11 ⋊ D5×D47 |
| Sylow | C5 ⋊ C2×D517 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C47 | C22 |
| LCS | G ▷ C5×C11×C47 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D517, D15×D517, D5×D1551, … |
| maximal normal subgroup of | C3×D5×D517 |
| maximal quotient of | C3×D5×D517, D15×D517, D5×D1551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10340, 28);